This is a 6 handed Micro 0.02-0.05 game in Bovada (no HUDs)
Middle has $1.02
I have $5.86 in the small blind.
And there's a nit with $13.12 in the big blind.
Action gets folded to middle position who goes all in for $1.02 and it gets folded to me.
I get dealt Pocket kings in the small blind.
I'm pretty happy just call. Worst cases it's Aces, I still have 20%, and way ahead of other pocket pairs. I decide to call, almost fully knowing that The bb is going to fold, because he played about 10% of hands (just an estimate). However, he decides to bump it up to $3.01 which is a pot sized raise. I call, really hoping it's not aces.
Calling leaving me with $2.85 in a $6.46 pot. So I'm fully committed.
The flop comes AcJcQh, I decided to push the rest in. I was going to call a bet anyway might as well bet it out myself. The big blind insta-calls showing me Trip aces. The turn comes a king of clubs and the river is a five of hearts. The Middle position shows Nines and so BB takes home $12.16.
Anything I could've done differently?

just push over bb pre

This is just one of those nasty spots in poker that will come around a few times a year. Nothing you can do. I would just shove pre flop hope the guy doesn't have aces. If he does keep playing and hopefully you will be on the other end sometime soon.

Shove pre, no reason to just flat lol

If calling the 3-bet commits you to stacking off on the flop, 4-bet jam pre. On the rare occasions where villain has QQ/JJ or AK, he might not be committed on boards where you're gonna stick the rest in, so you're kind of giving yourself a negative freeroll. You always get stacked if you flop second best, but you don't always stack villain if you have him beat.

Thanks guys, I learned something good out of it.